Re: Four color theorem: why this is not a proof and pointer to simple explanations
- From: riderofgiraffes <mathforum.org_am@xxxxxxxxxxxxxx>
- Date: Fri, 15 Jun 2007 09:58:06 EDT
Andre,
I think it's fantastic that you're encouraging your
son like this. Long may it continue. His reasoning
is generally pretty good, but there are, as you
suspect, a false step or two.
Here's the first one.
1. If there is a map where 5 colors are
needed, it must be because 5 different
countries are touching each other.
OK. Let's change that a little like this:
If there is a map that requires three
colors, then it must be because there
are three countries that all touch each
other.
Well, that turns out not to be the case.
Take a circle and cut it into five equal
pieces. This requires three colors, and
yet you cannot find three countries that
all touch each other.
Hope that helps to make it clear.
.
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